from sympy.combinatorics.group_numbers import (is_nilpotent_number,
    is_abelian_number, is_cyclic_number)
from sympy.testing.pytest import raises
from sympy import randprime


def test_is_nilpotent_number():
    assert is_nilpotent_number(21) == False
    assert is_nilpotent_number(randprime(1, 30)**12) == True
    raises(ValueError, lambda: is_nilpotent_number(-5))


def test_is_abelian_number():
    assert is_abelian_number(4) == True
    assert is_abelian_number(randprime(1, 2000)**2) == True
    assert is_abelian_number(randprime(1000, 100000)) == True
    assert is_abelian_number(60) == False
    assert is_abelian_number(24) == False
    raises(ValueError, lambda: is_abelian_number(-5))


def test_is_cyclic_number():
    assert is_cyclic_number(15) == True
    assert is_cyclic_number(randprime(1, 2000)**2) == False
    assert is_cyclic_number(randprime(1000, 100000)) == True
    assert is_cyclic_number(4) == False
    raises(ValueError, lambda: is_cyclic_number(-5))